On the Approximation of Positive Functions by Power

✍ Scribed by U. Schmid

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 124 KB
• Volume: 83
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1995.1125

✦ Synopsis

The problem to be studied goes back to a question of Erdös and Kövari, concerning functions (M(x), x \in R_{0}{ }^{+}), which are positive and logarithmically convex in (\ln x). The question to find necessary and sufficient conditions for the existence of a power series

[
N(x)=\sum c_{n} x^{n}, c_{n} \geqslant 0 \text { with } d_{1} \leqslant M(x) / N(x) \leqslant d_{2}, x \geqslant 0, \text { where } d_{1}, d_{2} \in R^{+}
]

has been treated by several authors. The present paper concerns a generalization of this problem regarding positive functions (h(x), x \in R_{0}^{+}). 1995 Academic Press. Inc.